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An Algorithm for Parametric Quadric Patch Construction

In: Geometric Modelling

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  • Gudrun Albrecht

    (Université de Valenciennes, ENSIAME — Laboratoire MACS)

Abstract

An algorithm for constructing arbitrary parametric quadratic quadric triangles in rational Bézier form is presented. The algorithm does not require the knowledge of the underlying quadric, an important property in view of applying this method for the interpolation of triangulated 3D data points. The algorithm consists of four steps starting with the arbitrary choice of the three corner points and corner weights of the patch, by then constructing a certain triangle and a tetrahedron by means of which the remaining inner control points and weights are obtained guaranteeing the resulting patch to lie on a quadric surface.

Suggested Citation

  • Gudrun Albrecht, 2004. "An Algorithm for Parametric Quadric Patch Construction," Springer Books, in: Stefanie Hahmann & Guido Brunnett & Gerald Farin & Ron Goldman (ed.), Geometric Modelling, pages 1-12, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-0587-0_1
    DOI: 10.1007/978-3-7091-0587-0_1
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